Question

An excited state of $H$ atom emits a photon of wavelength $\lambda$ and returns in the ground state, the principal quantum number of excited state is given by:

• A. $\sqrt{\lambda R(\lambda R-1)}$
• B. $\sqrt{\frac{\lambda R}{(\lambda R-1)}}$
• C. $\sqrt{\lambda R(\lambda R-1)}$
• D. $\sqrt{\frac{(\lambda R-1)}{\lambda R}}$

Answer 1

The correct option is B $\sqrt{\frac{\lambda R}{(\lambda R-1)}}$

By using the formula,
$\frac{1}{\lambda }=R(\frac{1}{n_1^2}-\frac{1}{n_2^2});n_1=1,n_2=?;\frac{1}{\lambda }=R(\frac{1}{1}-\frac{1}{n_2^2})\Rightarrow n_2^2=\frac{R\lambda }{R\lambda -1}\Rightarrow n_2=\sqrt{\frac{\lambda R}{\lambda R-1}}$